Related papers: Computational Notes on the Numerical Analysis of G…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
The rotation curve of a magnetized plasma cloud orbiting in the gravitational potential of a galaxy is calculated by statistical arguments. The working assumption is that a mild magnetic field, decreasing with distance from the galactic…
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous…
Galaxy simulations have come a long way from the early days of simple N-body calculations, which considered only gravitational interactions, to the complex, multi-physics models used today. Beginning with initial conditions representative…
Radiative processes such as synchrotron radiation and Compton scattering play an important role in astrophysics. Radiative processes are fundamentally stochastic in nature, and the best tools currently used for resolving these processes…
We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses.…
Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to…
This volume contains a selection of the papers presented at TERMGRAPH 2018, the tenth edition of the international workshop on computing with terms and graphs. Graphs, and graph transformation systems, are used in many areas within Computer…
The aim of this article is to show, how computer algebra can be used when applying Liu's procedure. Although Mathematica (a commercial product by Wolfram Research Inc.) is used, it is possible to use other computer algebra systems as well.
The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became…
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a…
In a previous work (Mbelek 2001), we modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion of the stars the dynamical terms from an external real self-interacting scalar field, $\psi$, minimally coupled…
Some issues of inverting asteroseismic frequency data are discussed, including the use of model calibration and linearized inversion. An illustrative inversion of artificial data for solar-type stars, using least-squares fitting of a small…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
Photometric rotational modulations due to starspots remain the most common and accessible way to study stellar activity. In the Kepler-era, there now exists precise, continuous photometry of ~150,000 stars presenting an unprecedented…
We illustrate the use of the computer algebra system Macaulay2 for simplifications of classical unirationality proofs. We explicitly treat the moduli spaces of curves of genus g=10, 12 and 14.
Two papers recently published in Celestial Mechanics (Krasinsky 2006, and Krasinsky and Vasilyev 2006) have presented a model for Earth-rotation variations, called ERA-2005, based on numerical integration of a new set of equations for the…
In a previous work \cite{mbeleka}, we have modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion dynamical terms from an external real self-interacting scalar field, $\phi$, minimally coupled to gravity…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…